Materials with very high hydrogen density have attracted considerable interest due to a range of motivations, including the search for chemically precompressed metallic hydrogen and hydrogen storage applications. Using high-pressure synchrotron X-ray diffraction technique and theoretical calculations, we have discovered a new rhodium dihydride (RhH(2)) with high volumetric hydrogen density (163.7 g/L). Compressing rhodium in fluid hydrogen at ambient temperature, the fcc rhodium metal absorbs hydrogen and expands unit-cell volume by two discrete steps to form NaCl-typed fcc rhodium monohydride at 4 GPa and fluorite-typed fcc RhH(2) at 8 GPa. RhH(2) is the first dihydride discovered in the platinum group metals under high pressure. Our low-temperature experiments show that RhH(2) is recoverable after releasing pressure cryogenically to 1 bar and is capable of retaining hydrogen up to 150 K for minutes and 77 K for an indefinite length of time.